Ring Resonator Design
Ring laser cavity of N curved mirrors: free spectral range, finesse, linewidth, photon lifetime, stability and the astigmatic mode sizes from the tilted mirrors.
Free spectral range c/L
999.3 MHz
Finesse ℱ = π ρ^¼/(1 − √ρ)
102.4
Round-trip power factor ρ = 0.9405
Linewidth (FWHM)
9.757 MHz
Q = ν/Δν = 2.89e7
Photon lifetime
16.31 ns
Threshold round-trip gain 1/ρ = 1.063
Angle of incidence on each mirror
30.00°
Segment d = L/N = 100.0 mm
Effective radius R_t / R_s
866.0 / 1155 mm
R cos α in the ring plane, R/cos α across it
Spot on mirrors: tangential / sagittal
269.4 µm / 288.4 µm
Waist mid-segment: tangential / sagittal
261.6 / 282.1 µm
Ellipticity w_s/w_t on the mirrors 1.07
ρ = Roc(1 − loss); intracavity power ∝ 1/(1 + F sin²(πΔν/FSR)), F = 4√ρ/(1 − √ρ)²; τ = (L/c)/(−ln ρ).
Period matrix free(d)·mirror(Reff): m = 1 − d/Reff, stable for |m| < 1, spot on the mirror w² = (λd/π)/√(1 − m²). α = 90° − 180°/N.
Cavity resonances over ±1.5 FSR
- Intracavity power / peak
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
N identical concave mirrors on a regular polygon, one output coupler. Finesse and linewidth from the Airy response of a one-way ring; modes from the paraxial period matrix with R cos α and R/cos α for the tilted mirrors. Image rotation in non-planar rings and thermal lensing are not modelled.
- Kogelnik H., Ippen E. P., Dienes A., Shank C. V. (1972). Astigmatically compensated cavities for CW dye lasers. IEEE J. Quantum Electron. 8, 373–379. doi:10.1109/jqe.1972.1076964
- Kogelnik H., Li T. (1966). Laser beams and resonators. Appl. Opt. 5, 1550–1567. doi:10.1364/ao.5.001550
- Siegman A. E. (1986). Lasers, ch. 11 and 21. University Science Books.